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IntegrationQuestion and Answers: Page 223

Question Number 64801 Answers: 0 Comments: 0

∫(cos^4 x+sin^4 x)/(cos2x+1)dx

$\int ({c o s}^{4} x + {s i n}^{4} x) / (c o s 2 x + 1) d x$

Question Number 64762 Answers: 1 Comments: 1

Given that g(x)=(2/((1+x)(1+3x^2 )) a) express g(x) in partial fractions. b) evaluate ∫_0 ^1 g((x) dx.

$Given that g (x) = \frac{2}{(1 + x) (1 + {3 x}^{2}}$ $a) express g (x) in partial fractions .$ $b) evaluate \int_{0}^{1} g ((x) dx .$

Question Number 64759 Answers: 0 Comments: 0

∫((ln(ln(x)))/((ln(x))^n )) dx , n≠1

$\int \frac{l n (l n (x))}{{(l n (x))}^{n}} d x, n \neq 1$

Question Number 64745 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((sin(lnx))/(lnx))dx

$c a l c u l a t e \int_{0}^{1} \frac{s i n (l n x)}{l n x} d x$

Question Number 64873 Answers: 0 Comments: 4

let f(x) =∫_0 ^π (dt/(x+sint)) with xreal 1) find a explicit form of f(x) 2) find also g(x) =∫_0 ^π (dt/((x+sint)^2 )) 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^π (dt/(3+sint)) and ∫_0 ^π (dt/((3+sint)^2 ))

$l e t f (x) = \int_{0}^{π} \frac{d t}{x + s i n t} w i t h x r e a l$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{π} \frac{d t}{{(x + s i n t)}^{2}}$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l$ $4) c a l c u l a t e \int_{0}^{π} \frac{d t}{3 + s i n t} a n d \int_{0}^{π} \frac{d t}{{(3 + s i n t)}^{2}}$

Question Number 64735 Answers: 0 Comments: 2

∫tanθ/1+^− sinθ dθ

$\int t a n θ / 1 \bar{+} s i n θ d θ$

Question Number 64733 Answers: 0 Comments: 0

∫(secθtanθ)dθ/secθ+^− tanθ

$\int (s e c θ t a n θ) d θ / s e c θ \bar{+} t a n θ$

Question Number 64687 Answers: 0 Comments: 1

Question Number 64677 Answers: 0 Comments: 4

let f(x) =∫_0 ^1 lnt ln(1−xt)dt with ∣x∣<1 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^1 ((tlnt)/(1−xt))dt 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^1 ln(t)ln(1−t)dt and ∫_0 ^1 ln(t)ln(2−t)dt 5) calculate ∫_0 ^1 ((tln(t))/(2−t)) dt .

$l e t f (x) = \int_{0}^{1} l n t l n (1 - x t) d t w i t h ∣ x ∣< 1$ $1) d e t e r m i n e a e x p l i c i t f o r m f o r f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{1} \frac{t l n t}{1 - x t} d t$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l$ $4) c a l c u l a t e \int_{0}^{1} l n (t) l n (1 - t) d t a n d \int_{0}^{1} l n (t) l n (2 - t) d t$ $5) c a l c u l a t e \int_{0}^{1} \frac{t l n (t)}{2 - t} d t .$

Question Number 64662 Answers: 1 Comments: 3

∫(dx/((x^8 +x^4 +1)^2 )) ∫_(1/x) ^x ((ln(t))/(t^2 +1)) dt

$\int \frac{d x}{{(x^{8} + x^{4} + 1)}^{2}}$ $\int_{\frac{1}{x}}^{x} \frac{l n (t)}{t^{2} + 1} d t$

Question Number 64649 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) ((cosθ)/(5+3cosθ))dθ

$c a l c u l a t e \int_{0}^{2 π} \frac{c o s θ}{5 + 3 c o s θ} d θ$

Question Number 64642 Answers: 0 Comments: 1

∫(dx)/e^x +x

$\int (d x) / e^{x} + x$

Question Number 64635 Answers: 0 Comments: 1

1)calculate f(a) =∫_0 ^∞ ((arctan(αx))/(1+x^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

$1) c a l c u l a t e f (a) = \int_{0}^{\infty} \frac{a r c t a n (α x)}{1 + x^{2}} d x w i t h α r e a l$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{a r c t a n (2 x)}{1 + x^{2}} d x$

Question Number 64579 Answers: 0 Comments: 1

∫ e^x^2 dx can we get a close form of this integral or analytic solution

$\int e^{x^{2}} dx$ $can we get a close form of this integral or analytic solution$

Question Number 64559 Answers: 0 Comments: 1

Question Number 64541 Answers: 1 Comments: 0

lol....QUESTION OF THE DAY SHOW FULL WORKINGS ∫x((((1−x^2 )Ln(1+x^2 )+(1+x^2 )−(1−x^2 )Ln(1−x^2 ))/((1−x^4 )(1+x^2 ))))e^((x^2 −1)/(x^2 +1)) dx

$l o l . . . . Q U E S T I O N O F T H E D A Y$ $S H O W F U L L W O R K I N G S$ $\int x (\frac{(1 - x^{2}) L n (1 + x^{2}) + (1 + x^{2}) - (1 - x^{2}) L n (1 - x^{2})}{(1 - x^{4}) (1 + x^{2})}) e^{\frac{x^{2} - 1}{x^{2} + 1}} d x$

Question Number 64529 Answers: 0 Comments: 0

calculate ∫_1 ^2 (dx/(√x)) by Rieman sum.

$c a l c u l a t e \int_{1}^{2} \frac{d x}{\sqrt{x}} b y R i e m a n s u m .$

Question Number 64528 Answers: 0 Comments: 1

find ∫_0 ^1 x^(−x) dx study first the convergence.

$f i n d \int_{0}^{1} x^{- x} d x s t u d y f i r s t t h e c o n v e r g e n c e .$

Question Number 64525 Answers: 0 Comments: 1

study the convergence of Σ U_n with U_n =∫_0 ^∞ ((cos(nx))/(x^2 +n^2 ))dx (n≥1)

$s t u d y t h e c o n v e r g e n c e o f Σ U_{n} w i t h$ $U_{n} = \int_{0}^{\infty} \frac{c o s (n x)}{x^{2} + n^{2}} d x (n ⩾ 1)$

Question Number 64477 Answers: 0 Comments: 1

pls i need it urgently... am stuck workings please (1) ∫Ln(1−Lnx)dx (2) ∫(1/(Lnx))dx (3)∫ Ln(−2Lnx)dx God will honour u 4 ur replies

$p l s i n e e d i t u r g e n t l y . . . a m s t u c k$ $w o r k i n g s p l e a s e$ $(1) \int L n (1 - L n x) d x$ $(2) \int \frac{1}{L n x} d x$ $(3) \int L n (- 2 L n x) d x$ $G o d w i l l h o n o u r u 4 u r r e p l i e s$

Question Number 64463 Answers: 0 Comments: 1

∫(√(sec(x))) dx

$\int \sqrt{s e c (x)} d x$

Question Number 64448 Answers: 1 Comments: 1

calculate lim_(x→π) ∫_(π/2) ^x (dx/(1+sinx−cosx))

$c a l c u l a t e {l i m}_{x \to π} \int_{\frac{π}{2}}^{x} \frac{d x}{1 + s i n x - c o s x}$

Question Number 64429 Answers: 0 Comments: 5

let f(x)=∫_0 ^1 (dt/(t+x+(√(t^2 +1)))) (x real parametre) 1) find a explicite form forf(x) 2)detemine also g(x) =∫_0 ^1 (dt/((t+x+(√(t^2 +1)))^2 )) 3)give f^((n)) (x) at form of integrals 4) find the values of ∫_0 ^1 (dt/(t+(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+(√(t^2 +1)))^2 )) 5) find the values of ∫_0 ^1 (dt/(t+1 +(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+1+(√(t^2 +1)))^2 ))

$l e t f (x) = \int_{0}^{1} \frac{d t}{t + x + \sqrt{t^{2} + 1}} (x r e a l p a r a m e t r e)$ $1) f i n d a e x p l i c i t e f o r m f o r f (x)$ $2) d e t e m i n e a l s o g (x) = \int_{0}^{1} \frac{d t}{{(t + x + \sqrt{t^{2} + 1})}^{2}}$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l s$ $4) f i n d t h e v a l u e s o f \int_{0}^{1} \frac{d t}{t + \sqrt{t^{2} + 1}} a n d \int_{0}^{1} \frac{d t}{{(t + \sqrt{t^{2} + 1})}^{2}}$ $5) f i n d t h e v a l u e s o f \int_{0}^{1} \frac{d t}{t + 1 + \sqrt{t^{2} + 1}} a n d \int_{0}^{1} \frac{d t}{{(t + 1 + \sqrt{t^{2} + 1})}^{2}}$

Question Number 64419 Answers: 0 Comments: 1

1) find ∫ (dx/(x−(√(1−x^2 )))) 2) calculate ∫_0 ^1 (dx/(x−(√(1−x^2 ))))

$1) f i n d \int \frac{d x}{x - \sqrt{1 - x^{2}}}$ $2) c a l c u l a t e \int_{0}^{1} \frac{d x}{x - \sqrt{1 - x^{2}}}$

Question Number 64418 Answers: 0 Comments: 3

1)find ∫ (dx/(x+(√(1+x^2 )))) 2) calculate ∫_0 ^1 (dx/(x+(√(1+x^2 ))))

$1) f i n d \int \frac{d x}{x + \sqrt{1 + x^{2}}}$ $2) c a l c u l a t e \int_{0}^{1} \frac{d x}{x + \sqrt{1 + x^{2}}}$

Question Number 64410 Answers: 1 Comments: 2

∫1/(1+ysinθ)dθ

$\int 1 / (1 + y s i n θ) d θ$

Pg 218 Pg 219 Pg 220 Pg 221 Pg 222 Pg 223 Pg 224 Pg 225 Pg 226 Pg 227

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